Question

Write $\dfrac{-14}{42}$ in the form so that the numerator is equal to – 70.

Answer 1

Hint: Now to convert the given fraction into a fraction with numerator – 70 we will have to multiply the numerator and denominator by some appropriate number. to find the appropriate number we will divide – 70 by – 14. Hence we can convert the fraction into the required fraction.

Complete step by step answer:
First let us understand the meaning of fractions.
Fractions are nothing but a part of a whole.
For example consider the fraction $\dfrac{3}{4}$ here the fractions means 3 parts out of 4. Now here in this fraction 3 is called the numerator of the fraction and 4 is called the denominator of the fraction.
Now when we multiply any number to the numerator and denominator the value of fraction does not change.
Hence let us say we multiply 2 then $\dfrac{3\times 2}{4\times 2}=\dfrac{6}{8}$ is same fraction as $\dfrac{3}{4}$ .
Hence by multiplying or dividing the numerator and denominator by common number the value of fraction does not change.
Now consider the given fraction $\dfrac{-14}{42}$ . Here the numerator of the fraction is – 14 and the denominator of the fraction is 42.
Now we want the numerator of this fraction to be – 70.
Hence to do so we will multiply the numerator with a number such that the multiplication becomes – 70.
Let the required number be n.
Hence we want $-14\times n=-70$ .
Dividing the equation by – 14 we get n = 5.
Now that we have the required number we will multiply the numerator and denominator by 5.
Hence we get $\dfrac{-14\times 5}{42\times 5}=\dfrac{-70}{210}$ .
Hence the required fraction is $\dfrac{-70}{210}$ .

Note: Note that when we add and subtract the fractions their denominator must be the same. For fractions with the same denominator we have $\dfrac{a}{b}\pm \dfrac{c}{b}=\dfrac{a\pm c}{b}$ . If we have fractions with different denominators we will multiply the numerator and denominator by LCM of denominators so that we get common denominators.